摘要：In this paper a special complex Kn of abstract cubes [2, 3], which contains only n -dimensional cubes is examined. The border of this complex is an abstract ( n −1)-dimensional sphere. It is proved that the abstract sphere contains at least one 0-dimensional cube, which belongs to exactly n cubes with dimension 1, if the complex is a homogeneous n -dimensional tree. This result allows to solve, in an efficient way, the problem of median for a skeleton of size 1 of the tree with weighted vertices and edges. The algorithm to calculate the median without using any metric is described. The proposed algorithm can be applied with some modifications, for arbitrary complex of abstract cubes.
关键词：Abstract cube; complex; multidimensional homogeneous tree; abstract sphere; median
